Acyclic Chromatic Indices of Planar Graphs with Girth At Least 4

Authors


  • Contract grant sponsor: NSFC; Contract grant numbers: 11071223; 61170302; Contract grant sponsor: ZJNSFC; Contract grant number: Z6090150; Contract grant sponsor: ZJIP; Contract grant number: T200905; Contract grant sponsors: ZSDZZZZXK13; IP-OCNS-ZJNU.

Abstract

An acyclic edge coloring of a graph G is a proper edge coloring such that no bichromatic cycles are produced. The acyclic chromatic index math formula of G is the smallest integer k such that G has an acyclic edge coloring using k colors. Fiammath formulaik (Math. Slovaca 28 (1978), 139–145) and later Alon et al. (J Graph Theory 37 (2001), 157–167) conjectured that math formula for any simple graph G with maximum degree Δ. In this article, we confirm this conjecture for planar graphs of girth at least 4.

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